Abstract: This proposed minisymposium is about the development and application of reduced-order modeling techniques in the fields of uncertainty quantification and computational fluid dynamics for control, optimization and design. Large-scale computing is commonly faced in these fields due to the high computational complexity of solving parametric and/or stochastic systems described by, e.g. partial different equations, which may lead to unaffordable computational burden for real-world application. In order to tackle this challenge, reduced-order modeling (e.g. RB, POD, EIM, PGD) techniques with the aim of capturing and utilizing the most important features of these systems are particularly in need for real-time and/or many-query computing.

Reduced-order modeling techniques have undergone fast development during the last decade and become a new frontier in scientific computing. Their increasing popularity is witnessed by many minisymposia at congress and conferences around the world, such as ICIAM, ICOSAHOM, WCCM, SIAM CSE, SIAM UQ, ECCOMAS, ENUMATH. The aim of this minisymposium is to discuss the most recent development of these techniques with emphasis in the field of UQ and CFD and identify new directions and perspectives. For this purpose we have invited 12 speakers with great expertise from several universities around the world, e.g. (MIT, Stanford, Paris VI, EPFL, TU Munich, CAS, Sandia National Laboratories, etc.)

MS-Mo-D-32-113:30--14:00Introduction of reduced-order modeling for UQ and CFDRozza, Gianluigi (SISSA, International School for Advanced Studies)Chen, Peng (ETH Zurich (Swiss Federal Inst. of Tech. in Zurich))Abstract: We present some recent development of reduced-order modeling techniques in the fields of uncertainty quantification and computational fluid dynamics. We consider multilevel and weighted algorithms in the context of reduced-order modeling to capture and utilize the most important features of the underlying systems. Examples of high-dimensional variational data assimilation for blood flow in carotid artery will be shown to demonstrate the efficiency and accuracy of our proposed algorithms.

MS-Mo-D-32-214:00--14:30Dynamical low rank approximation of incompressible Navier Stokes
equations with random parametersMusharbash, Eleonora (EPFL)Nobile, Fabio (MATHICSE - EPFL)Abstract: We propose a Reduced Basis approach for time dependent incompressible Navier Stokes equations
with random parameters, based on a time evolving, Dynamically Orthogonal, basis. The solution is
approximated in a low dimensional, time dependent manifold MS. This is achieved by projecting
at each time step the residual of the governing equation onto the tangent space to MS. Numerical
tests at moderate Reynold number will be presented, with emphasis on the case of stochastic boundary conditions.

MS-Mo-D-32-314:30--15:00Adaptive model reduction for large-scale inverse problems with high dimensional unknowns.Cui, Tiangang (MIT)Marzouk, Youssef (Massachusetts Inst. of Tech.)Willcox, Karen (MIT)Abstract: Algorithmic scalability to high dimensional parameters and computational efficiency of numerical solvers are two significant challenges in large-scale, PDE-constrained inverse problems. Here we will explore the intrinsic dimensionality in both state space and parameter space of inverse problems by analyzing the interplay between noisy data, ill-posed forward model and smoothing prior. The resulting reduced subspaces naturally lead to a scalable and fast model reduction framework for solving large-scale inverse problems with high dimensional parameters.

MS-Mo-D-32-415:00--15:30Hybridized Reduced Basis Method and Generalized Polynomial Chaos for Solving Partial Differential EquationsJiang, Jiahua (Univ. of Massachusetts Dartmouth)Abstract: The generalized Polynomial Chaos (gPC) method is a popular method for solving partial differential equations (PDEs) with random parameters. However, when the probability space has high dimensionality, the solution ensemble size required for an accurate gPC approximation can be large. We show that this process can be made more efficient by closely hybridizing gPC with Reduced Basis Method (RBM). Since the reduced model is more efficient, costs are significantly reduced.